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CadwalladerOlsker, Todd – Mathematics Teacher, 2019

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

Descriptors: Statistics, Mathematics Education, Misconceptions, Hypothesis Testing

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam – Mathematics Teacher, 2018

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

Descriptors: Mathematics Instruction, Mathematical Models, Learner Engagement, Secondary School Mathematics

Gleason, Brian – Mathematics Teacher, 2018

In this article, a mathematics teacher educator presents an activity designed to pique the interest of prospective secondary mathematics teachers who may doubt the value of learning abstract algebra for their chosen profession. Herein, he contemplates: what "is" intended by the widespread requirement that high school mathematics teachers…

Descriptors: Mathematics Instruction, Mathematics Teachers, Teacher Educators, Secondary Education

Murray, Natasha T. K. – Mathematics Teacher, 2018

How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…

Descriptors: Mathematical Concepts, Number Concepts, Algebra, Mathematics Instruction

Sun, Kathy L.; Baldinger, Erin E.; Humphreys, Cathy – Mathematics Teacher, 2018

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…

Descriptors: Mathematics Instruction, Secondary School Mathematics, High School Students, Concept Formation

Quinn, Anne – Mathematics Teacher, 2016

While looking for an inexpensive technology package to help students in statistics classes, the author found StatKey, a free Web-based app. Not only is StatKey useful for students' year-end projects, but it is also valuable for helping students learn fundamental content such as the central limit theorem. Using StatKey, students can engage in…

Descriptors: Statistics, Computer Oriented Programs, Technology Uses in Education, Teaching Methods

Lancaster, Ron – Mathematics Teacher, 2016

Can you solve the following Problem? There are 200 fish in an aquarium, and 99 percent of them are guppies. How many guppies must be removed to reduce the tank's guppy population to 98 percent? The key to this problem is to work backward by using the data given in figure 2 to determine the surface area of the top of the aquarium; then determine…

Descriptors: Mathematics Instruction, Problem Solving, Word Problems (Mathematics), Equations (Mathematics)

Hurdle, Zach; Warshauer, Max; White, Alex – Mathematics Teacher, 2016

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

Descriptors: Mathematics Instruction, Mathematics Activities, Mathematical Formulas, Computation

Gilbertson, Nicholas J. – Mathematics Teacher, 2016

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

Descriptors: Mathematics Instruction, Mathematical Formulas, Validity, Mathematical Logic

Reed, Cameron – Mathematics Teacher, 2016

How can old-fashioned tables of logarithms be computed without technology? Today, of course, no practicing mathematician, scientist, or engineer would actually use logarithms to carry out a calculation, let alone worry about deriving them from scratch. But high school students may be curious about the process. This article develops a…

Descriptors: Mathematics Instruction, Computation, Numbers, Mathematical Concepts

Wasserman, Nicholas H. – Mathematics Teacher, 2015

Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three…

Descriptors: Mathematics Instruction, Mathematical Concepts, Statistics, Probability

Strayer, Jeremy F.; Edwards, Michael Todd – Mathematics Teacher, 2015

A news story claiming that the cream filling of a popular "double" cream sandwich cookie is not really "double" went viral in fall 2013. A high school mathematics teacher posted a blog entry describing how he and his students measured 20 cookies, analyzed the data, and concluded that the double cream cookies had only 1.86 times…

Descriptors: Media Literacy, News Media, Mathematics Education, Statistics

Anhalt, Cynthia Oropesa; Cortez, Ricardo – Mathematics Teacher, 2015

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Descriptors: Mathematics Instruction, Mathematical Models, Teaching Methods, Mathematical Concepts

Marion, Charles F. – Mathematics Teacher, 2015

This analysis of a problem that is frequently posed at professional development workshops, in print, and on the Web--the coffee-milk mixture riddle--illustrates the timeless advice of George Pólya's masterpiece on problem solving in mathematics, "How to Solve It." In his book, Pólya recommends that problems previously solved and put…

Descriptors: Problem Solving, Teaching Methods, Mathematical Concepts, Computation

Bismarck, Stephen F.; Zelkowski, Jeremy; Gleason, Jim – Mathematics Teacher, 2014

Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninety-minute block or two forty-five-minute classes, students build functions…

Descriptors: Mathematics Instruction, Prediction, Fuels, Algebra